Entanglement Entropy in 2D Non-abelian Pure Gauge Theory

Gromov, Andrey; Santos, Raul A.

doi:10.1016/j.physletb.2014.08.023

Entanglement Entropy in 2D Non-abelian Pure Gauge Theory

Andrey Gromov
(
- SUNY, Stony Brook
)
,
Raul A. Santos
(
- YITP, Stony Brook
)

Mar 19, 2014

5 pages

Published in:

Phys.Lett.B 737 (2014) 60-64

Published: Oct 7, 2014

e-Print:

1403.5035 [hep-th]

DOI:

10.1016/j.physletb.2014.08.023

View in:

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Abstract: (Elsevier)

We compute the Entanglement Entropy (EE) of a bipartition in 2D pure non-abelian U(N) gauge theory. We obtain a general expression for EE on an arbitrary Riemann surface. We find that due to area-preserving diffeomorphism symmetry EE does not depend on the size of the subsystem, but only on the number of disjoint intervals defining the bipartition. In the strong coupling limit on a torus we find that the scaling of the EE at small temperature is given by S(T)−S(0)=O(mgapTe−mgapT) , which is similar to the scaling for the matter fields recently derived in literature. In the large N limit we compute all of the Renyi entropies and identify the Douglas–Kazakov phase transition.

Note:

6 pages

Gauge theories
Entropy
Entanglement
entropy: entanglement
approximation: strong coupling
gauge field theory
scaling
gap
critical phenomena
Riemann surface

References(34)

Figures(0)

Universal Thermal Corrections to Single Interval Entanglement Entropy for Two Dimensional Conformal Field Theories

John Cardy
(
- Oxford U., Theor. Phys. and
- Oxford U.
)
,
Christopher P. Herzog
(
- YITP, Stony Brook and
- Stony Brook U.
)

- Phys.Rev.Lett. 112 (2014) 17, 171603
•
e-Print:
- 1403.0578
•
DOI:
- 10.1103/PhysRevLett.112.171603

[19]

Recursion Equations in Gauge Theories

Alexander A. Migdal
(
- Landau Inst.
)

- Sov.Phys.JETP 42 (1975) 413,
- Zh.Eksp.Teor.Fiz. 69 (1975) 810-822,

[18]

Lectures on 2-d Yang-Mills theory, equivariant cohomology and topological field theories

- Nucl.Phys.B Proc.Suppl. 41 (1995) 184-244,
- Trieste Spring School 1994:0184-244,
- Trieste Spring School 1994:0184-244
•
e-Print:
- hep-th/9411210
•
DOI:
- 10.1016/0920-5632(95)00434-B

[15]

Two-dimensional QCD is a string theory

David J. Gross
(
- Princeton U. and
- LBL, Berkeley
)
,
Washington Taylor
(
- UC, Berkeley and
- LBL, Berkeley
)

- Nucl.Phys.B 400 (1993) 181-208
•
e-Print:
- hep-th/9301068
•
DOI:
- 10.1016/0550-3213(93)90403-C

[7]

Black hole entropy and entropy of entanglement

Daniel N. Kabat
(
- Rutgers U., Piscataway
)

- Nucl.Phys.B 453 (1995) 281-299
•
e-Print:
- hep-th/9503016
•
DOI:
- 10.1016/0550-3213(95)00443-V

Entanglement entropy and quantum field theory

Pasquale Calabrese
(
- Oxford U., Theor. Phys.
)
,
John L. Cardy
(
- Oxford U., Theor. Phys. and
- Oxford U.
)

- J.Stat.Mech. 0406 (2004) P06002
•
e-Print:
- hep-th/0405152
•
DOI:
- 10.1088/1742-5468/2004/06/P06002

[1]

Entanglement in many-body systems

Luigi Amico
(
- Catania U., DMFCI
)
,
Rosario Fazio
(
- NEST-INFM and
- SISSA, Trieste
)
,
Andreas Osterloh
(
- Hannover U.
)
,
Vlatko Vedral
(
- Leeds U.
)

- Rev.Mod.Phys. 80 (2008) 517-576
•
e-Print:
- quant-ph/0703044
•
DOI:
- 10.1103/RevModPhys.80.517

[2]

On geometric entropy

- Phys.Lett.B 333 (1994) 55-61
•
e-Print:
- hep-th/9401072
•
DOI:
- 10.1016/0370-2693(94)91007-3

[3]

Entanglement entropy and quantum field theory,

P. Calabrese
,
J. Cardy

[4]

Entanglement as a probe of confinement

Igor R. Klebanov
(
- Princeton U. and
- Princeton U., CTP
)
,
David Kutasov
(
- Chicago U.
)
,
Arvind Murugan
(
- Princeton U. and
- Princeton U., CTP
)

- Nucl.Phys.B 796 (2008) 274-293
•
e-Print:
- 0709.2140
•
DOI:
- 10.1016/j.nuclphysb.2007.12.017

[5]

Entanglement entropy in gauge theories and the holographic principle for electric strings

P.V. Buividovich
(
- Joint Inst. Power Nucl. Res., Minsk and
- Moscow, ITEP
)
,
M.I. Polikarpov
(
- Moscow, ITEP
)

- Phys.Lett.B 670 (2008) 141-145
•
e-Print:
- 0806.3376
•
DOI:
- 10.1016/j.physletb.2008.10.032

[6]

Decomposition of entanglement entropy in lattice gauge theory

William Donnelly
(
- Maryland U.
)

- Phys.Rev.D 85 (2012) 085004
•
e-Print:
- 1109.0036
•
DOI:
- 10.1103/PhysRevD.85.085004

[7]

Black hole entropy and entropy of entanglement

Daniel N. Kabat
(
- Rutgers U., Piscataway
)

- Nucl.Phys.B 453 (1995) 281-299
•
e-Print:
- hep-th/9503016
•
DOI:
- 10.1016/0550-3213(95)00443-V

[8]

Numerical study of entanglement entropy in SU(2) lattice gauge theory

P.V. Buividovich
(
- Joint Inst. Power Nucl. Res., Minsk and
- Moscow, ITEP
)
,
M.I. Polikarpov
(
- Moscow, ITEP
)

- Nucl.Phys.B 802 (2008) 458-474
•
e-Print:
- 0802.4247
•
DOI:
- 10.1016/j.nuclphysb.2008.04.024

[9]

Do gauge fields really contribute negatively to black hole entropy?

William Donnelly
(
- Maryland U.
)
,
Aron C. Wall
(
- UC, Santa Barbara
)

- Phys.Rev.D 86 (2012) 064042
•
e-Print:
- 1206.5831
•
DOI:
- 10.1103/PhysRevD.86.064042

[10]

Topological entanglement entropy

Alexei Kitaev
(
- Caltech, IQI and
- Microsoft, Redmond
)
,
John Preskill
(
- Caltech, IQI
)

- Phys.Rev.Lett. 96 (2006) 110404
•
e-Print:
- hep-th/0510092
•
DOI:
- 10.1103/PhysRevLett.96.110404

[11]

Detecting Topological Order in a Ground State Wave Function

Michael Levin
(
- MIT
)
,
Xiao-Gang Wen
(
- MIT
)

- Phys.Rev.Lett. 96 (2006) 110405
•
e-Print:
- cond-mat/0510613
•
DOI:
- 10.1103/PhysRevLett.96.110405

[12]

Topological entanglement entropy of a Bose–Hubbard spin liquid

- Nature Phys. 7 (2011) 10, 772-775
•
DOI:
- 10.1038/nphys2036

[13]

Symmetry protected topological orders and the group cohomology of their symmetry group

Xie Chen
(
- MIT, LNS and
- UC, Berkeley (main)
)
,
Zheng-Cheng Gu
(
- Caltech
)
,
Zheng-Xin Liu
(
- Tsinghua U., Beijing and
- MIT, LNS
)
,
Xiao-Gang Wen
(
- MIT, LNS and
- Tsinghua U., Beijing and
- Perimeter Inst. Theor. Phys.
)

- Phys.Rev.B 87 (2013) 15, 155114
•
e-Print:
- 1106.4772
•
DOI:
- 10.1103/PhysRevB.87.155114

[14]

Remarks on entanglement entropy for gauge fields

- Phys.Rev.D 89 (2014) 8, 085012
•
e-Print:
- 1312.1183
•
DOI:
- 10.1103/PhysRevD.89.085012

[15]

Two-dimensional QCD is a string theory

David J. Gross
(
- Princeton U. and
- LBL, Berkeley
)
,
Washington Taylor
(
- UC, Berkeley and
- LBL, Berkeley
)

- Nucl.Phys.B 400 (1993) 181-208
•
e-Print:
- hep-th/9301068
•
DOI:
- 10.1016/0550-3213(93)90403-C

[16]

Geometric and renormalized entropy in conformal field theory

Christoph Holzhey
(
- Princeton U.
)
,
Finn Larsen
(
- Princeton U.
)
,
Frank Wilczek
(
- Princeton, Inst. Advanced Study
)

- Nucl.Phys.B 424 (1994) 443-467
•
e-Print:
- hep-th/9403108
•
DOI:
- 10.1016/0550-3213(94)90402-2

[17]

Loop averages and partition functions in U(N) gauge theory on two-dimensional manifolds

B.E. Rusakov
(
- Moscow, Cybernetics Council
)

- Mod.Phys.Lett.A 5 (1990) 693-703
•
DOI:
- 10.1142/S0217732390000780

[18]

Lectures on 2-d Yang-Mills theory, equivariant cohomology and topological field theories

- Nucl.Phys.B Proc.Suppl. 41 (1995) 184-244,
- Trieste Spring School 1994:0184-244,
- Trieste Spring School 1994:0184-244
•
e-Print:
- hep-th/9411210
•
DOI:
- 10.1016/0920-5632(95)00434-B

[19]

Recursion Equations in Gauge Theories

Alexander A. Migdal
(
- Landau Inst.
)

- Sov.Phys.JETP 42 (1975) 413,
- Zh.Eksp.Teor.Fiz. 69 (1975) 810-822,

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